Cost-Based Optimization of Integration Flows - Datenbanken ...

6 On-Demand Re-Optimization
f γ((γR)⋊⋉S) θ f γ(R⋊⋉S) /f γ(R) . If we assume independence for this group-by selectivity, we
have f γ((γR)⋊⋉S) = 1 and can set f γ(R⋊⋉S) = f γ(R) . As a result, we can derive all variables
of the optimality conditions from statistics of the optimal plan.
* |R|, |S| as additional input
R S γ
|R| |S| |R S| | γ(R S)|
fR,S
f γ(R ⋈ S)
γ
oc 2 oc 3
oc 4
C1 *C2
*C3
*C4
R
S
≤
(oc1)
≤
(oc2)
≤
(oc3)
≤
(oc4)
oc 1
(a) Example POT
(b) Optimality Conditions
(c) Complexity Analysis
Figure 6.10: Example Eager Group-By
Figure 6.10(a) shows the resulting PlanOptTree, where we omitted some connections
(*) to atomic statistic nodes for simplicity of presentation. Note that for eager group-by,
no transitivity is used. Furthermore, only the plan optimality is modeled rather than
the whole plan search space. Hence, only four optimality conditions are required per join
operator as shown in Figure 6.10(b). Accordingly, Figure 6.10(c) compares the number of
alternative plans of the full search space with the number of required optimality conditions.
The improvement is reasoned by the fact that for each join input, we just model if preaggregation
is advantageous or not.
Union Distinct Example
In contrast to join enumeration or eager group-by, there are many control-flow- and
data-flow-oriented optimization techniques with fairly simple optimality conditions and
thus, rather small PlanOptTrees. An example is the optimization technique WD11:
Setoperation-Type Selection (set operations with distinctness).
oc 2
U
sort(R)
R S R
oc 1
UM
sort(S)
S
(a) Union Distinct Alternatives
R U S
|R| |S| |R U S|
≤
(oc1)
C1
≥
(oc’2)
C2
(b) Example POT
Figure 6.11: Example Union Distinct
There are three alternative subplans for a union distinct R∪S. First, there is the normal
union distinct operator with costs that are given by C(R ∪ S) = |R| + |S| · |R ∪ S|/2 (two
plans due to asymmetric costs), where |R| ≤ |R ∪ S| ≤ |R| + |S| holds. Second, we can
sort both inputs and apply a merge algorithm with costs of
C (sort(R) ∪ M sort(S)) = |R| + |S| + |R| · log 2 |R| + |S| · log 2 |S|. (6.7)
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